Large eddy simulation of structural characteristics in turbulent flow around a circular cylinder close to a wavy wall

The flow characteristics and vortex evolution behind a circular cylinder near a wavy wall are studied using a large-eddy simulation framework. The Reynolds number based on the cylinder diameter D is ReD = 1500, the gap ratio G/D is fixed to 1, and the slope S = λ/2k varies from 2 to 8 (where G is the distance between the lower surface of the cylinder and the crest, λ is the wavelength, and k is the wave amplitude). The flow field characteristics, hydrodynamic coefficients, pressure distributions, vortex evolution, and three-dimensional flow features are presented and discussed. The phase of the flow field is determined by proper orthogonal decomposition, and the vortex identification method is applied to capture vortex structures. Compared with a smooth wall, the wavy wall changes the pressure distribution of the flow field and decreases (increases) the mean drag (lift) coefficient. As the wall amplitude increases, the Strouhal number increases slightly, attaining values of 0.25 for S = 8, 0.25 for S = 4, and 0.26 for S = 2. The wall pressure coefficient has an approximately periodic distribution, while the wall friction coefficient varies according to the evolution of secondary vortices on the wall. Two small secondary vortices appear either side of the crest before merging into a new secondary vortex that moves downstream with the upper and lower wake vortices. The energy of the first two modes obtained by proper orthogonal decomposition decreases compared with the smooth-wall case, whereas that of the third and fourth modes increases, reflecting the greater large-scale vortex structures between the wavy walls. This is confirmed by examining the instantaneous three-dimensional vortex structures using the Q-criterion.